November 22nd, 2014

eyes black and white

Personality Types for Mathematicians

When I was a kid, I used to believe that mathematics was all about knowing the rules and following them perfectly (which at least, unlike in other endeavours, was possible), and about carefully planning your strategy to attack and vanquish given problems, and that a good mathematician would be one who would primarily think like that. In terms of MBTI (which I didn't know at the time), that would be an INTJ personality, the Mastermind as Keirsey calls it. Since my dad was a math professor, I thought he had to be like that. But as I grew up, I realized to my surprise that wasn't the case. Indeed, while these activities are indeed essential in Mathematics, and any mathematician must be capable of thinking that way, and while some mathematicians have this personality indeed (including some friends of my father), my father himself was actually an INFP, a Healer in Keirsey speech. What made him love mathematics was the abstract aesthetics of it — how to discover and appreciate beautiful proofs, that only involved intrinsic aspects of the mathematical objects (points, lines, planes, curves, functions, etc.) rather than representation-dependent aspects (such as spatial coordinates in some arbitrary basis, or equations, etc.), and what interesting and beautiful properties those proofs told us about the underlying mathematical structure — the best ones being those that show deep connections between different structures. I find that I love computing the very same way. In terms of individual traits, I suppose that "Introversion" is necessary to focus on abstract mathematical objects (whereas "Extroversion" is more useful in collaborative programming settings), and so is "iNtuition" (which I understand as about approaching the world in abstract rather than concrete terms). "Thinking" is important to follow the rules, but "Feeling" is important to appreciate the aesthetics, which may be the greatest heuristic guide you can have in Mathematics. And "Judgment" might be useful for planning problem-solving strategies, but "Perception" is useful for getting a good sense of an unfamiliar world. [Interestingly, while I identify myself as ENTP, which Keirsey calls an Inventor, my wife is an INFP and most of my past girlfriends were, or were not far from it — it's the personality type I somehow most relate to, even though I obviously didn't relate enough to my father as a kid, since I didn't understand him at all then.]